Estimating variance components and heritabilities in the wild: a case study using the ‘animal model’ approach

Using a genealogy containing over 1800 dams and nearly 400 sires (estimated by genetic paternity techniques), combined with maximum likelihood procedures and an ‘animal model’, we have estimated the heritabilities, genetic correlations and variance components of three morphometric traits in the Soay sheep (Ovis aries) on St Kilda, Scotland. This approach allows heritabilities to be estimated in natural populations that violate the assumptions of offspring–parent regression methods. Maternal (or paternal) effects can also be estimated under natural conditions. We demonstrate that all the traits, body weight, hind leg length and incisor arcade breadth, have low but significant heritabilities. Body weight, the trait that experiences the strongest selection, had the lowest heritability but the highest additive genetic coefficient of variation. An evolutionary response to selection is predicted. When maternal effects were not taken into consideration heritabilities were over‐estimated, although this effect was only significant in female offspring.     

A framework for power and sensitivity analyses for quantitative genetic studies of natural populations, and case studies in Soay sheep (Ovis aries)

Studies of the quantitative genetics of natural populations have contributed greatly to evolutionary biology in recent years. However, while pedigree data required are often uncertain (i.e. incomplete and partly erroneous) and limited, means to evaluate the effects of such uncertainties have not been developed. We have therefore developed a general framework for power and sensitivity analyses of such studies. We propose that researchers first generate a set of pedigree data that they wish to use in a quantitative genetic study, as well as data regarding errors that occur in that pedigree. This pedigree is then permuted using the data regarding errors to generate hypothetical 'true' and 'assumed' pedigrees that differ so as to mimic pedigree errors that might occur in the study system under consideration. Phenotypic data are then simulated across the true pedigree (according to user-defined genetic and environmental covariance structures), before being analysed with standard quantitative genetic techniques in conjunction with the 'assumed' pedigree data. To illustrate this approach, we conducted power and sensitivity analyses in a well-known study of Soay sheep (Ovis aries). We found that, although the estimation of simple genetic (co)variance structures is fairly robust to pedigree errors, some potentially serious biases were detected under more complex scenarios involving maternal effects. Power analyses also showed that this study system provides high power to detect heritabilities as low as about 0.09. Given this range of results, we suggest that such power and sensitivity analyses could greatly complement empirical studies, and we provide the computer program PEDANTICS to aid in their application.     

Low heritabilities, but genetic and maternal correlations between red squirrel behaviours

Consistent individual differences in behaviour, and behavioural correlations within and across contexts, are referred to as animal personalities. These patterns of variation have been identified in many animal taxa and are likely to have important ecological and evolutionary consequences. Despite their importance, genetic and environmental sources of variation in personalities have rarely been characterized in wild populations. We used a Bayesian animal model approach to estimate genetic parameters for aggression, activity and docility in North American red squirrels (Tamiasciurus hudsonicus). We found support for low heritabilities (0.08-0.12), and cohort effects (0.07-0.09), as well as low to moderate maternal effects (0.07-0.15) and permanent environmental effects (0.08-0.16). Finally, we found evidence of a substantial positive genetic correlation (0.68) and maternal effects correlation (0.58) between activity and aggression providing evidence of genetically based behavioural correlations in red squirrels. These results provide evidence for the presence of heritable variation in red squirrel behaviour, but also emphasize the role of other sources of variation, including maternal effects, in shaping patterns of variation and covariation in behavioural traits.     

How to separate genetic and environmental causes of similarity between relatives

Related individuals often have similar phenotypes, but this similarity may be due to the effects of shared environments as much as to the effects of shared genes. We consider here alternative approaches to separating the relative contributions of these two sources to phenotypic covariances, comparing experimental approaches such as cross-fostering, traditional statistical techniques and more complex statistical models, specifically the 'animal model'. Using both simulation studies and empirical data from wild populations, we demonstrate the ability of the animal model to reduce bias due to shared environment effects such as maternal or brood effects, especially where pedigrees contain multiple generations and immigration rates are low. However, where common environment effects are strong, a combination of both cross-fostering and an animal model provides the best way to avoid bias. We illustrate ways of partitioning phenotypic variance into components of additive genetic, maternal genetic, maternal environment, common environment, permanent environment and temporal effects, but also show how substantial confounding between these different effects may occur. Whilst the flexibility of the mixed model approach is extremely useful for incorporating the spatial, temporal and social heterogeneity typical of natural populations, the advantages will inevitably be restricted by the quality of pedigree information and care needs to be taken in specifying models that are appropriate to the data.     

Quantitative genetics of sexually dimorphic traits and capture of genetic variance by a sexually-selected condition-dependent ornament in red junglefowl (Gallus gallus)

We studied the quantitative genetics of sexually selected traits in a captive population of red junglefowl (Gallus gallus L.) using a multi-generational 'animal model' approach. We found significant heritability of mass, tarsus length (both strongly sexually dimorphic), residual mass, and male comb (a fleshy head ornament) length. Residual mass has a genetic correlation between the sexes smaller than unity and so could show partially independent responses to selection in the two sexes. In males, tarsus length and mass were not genetically correlated, and this produced a negative genetic correlation between tarsus length and residual mass. The male red junglefowl's comb, an ornament influencing female choice, is highly condition dependent. We show that expression of this ornament is heritable, however, and shows strong genetic correlation with a condition index, residual mass. Because residual mass is partly influenced by various aspects of condition, it appears that comb size has 'captured' genetic variability in condition.     

Genetic parameters for litter size in sheep: natural versus hormone-induced oestrus

The litter size in Suffolk and Texel-sheep was analysed using REML and Bayesian methods. Litters born after hormonal induced oestrus and after natural oestrus were treated as different traits in order to estimate the genetic correlation between the traits. Explanatory variables were the age of the ewe at lambing, period of lambing, a year*flock-effect, a permanent environmental effect associated with the ewe, and the additive genetic effect. The heritability estimates for litter size ranged from 0.06 to 0.13 using REML in bi-variate linear models. Transformation of the estimates to the underlying scale resulted in heritability estimates from 0.12 to 0.17. Posterior means of the heritability of litter size in the Bayesian approach with bi-variate threshold models varied from 0.05 to 0.18. REML estimates of the genetic correlations between the two types of litter size ranged from 0.57 to 0.64 in the Suffolk and from 0.75 to 0.81 in the Texel. The posterior means of the genetic correlation (Bayesian analysis) were 0.40 and 0.44 for the Suffolk and 0.56 and 0.75 for the Texel in the sire and animal model respectively. A bivariate threshold model seems appropriate for the genetic evaluation of prolificacy in the breeds concerned.     

Genetic variances and covariances of aerobic metabolic rates in laboratory mice

The genetic variances and covariances of traits must be known to predict how they may respond to selection and how covariances among them might affect their evolutionary trajectories. We used the animal model to estimate the genetic variances and covariances of basal metabolic rate (BMR) and maximal metabolic rate (MMR) in a genetically heterogeneous stock of laboratory mice. Narrow-sense heritability (h²) was approximately 0.38 ± 0.08 for body mass, 0.26 ± 0.08 for whole-animal BMR, 0.24 ± 0.07 for whole-animal MMR, 0.19 ± 0.07 for mass-independent BMR, and 0.16 ± 0.06 for mass-independent MMR. All h² estimates were significantly different from zero. The phenotypic correlation of whole animal BMR and MMR was 0.56 ± 0.02, and the corresponding genetic correlation was 0.79 ± 0.12. The phenotypic correlation of mass-independent BMR and MMR was 0.13 ± 0.03, and the corresponding genetic correlation was 0.72 ± 0.03. The genetic correlations of metabolic rates were significantly different from zero, but not significantly different from one. A key assumption of the aerobic capacity model for the evolution of endothermy is that BMR and MMR are linked. The estimated genetic correlation between BMR and MMR is consistent with that assumption, but the genetic correlation is not so high as to preclude independent evolution of BMR and MMR.     

Quantitative genetics and sex-specific selection on sexually dimorphic traits in bighorn sheep

Sexual conflict at loci influencing traits shared between the sexes occurs when sex-specific selection pressures are antagonistic relative to the genetic correlation between the sexes. To assess whether there is sexual conflict over shared traits, we estimated heritability and intersexual genetic correlations for highly sexually dimorphic traits (horn volume and body mass) in a wild population of bighorn sheep (Ovis canadensis) and quantified sex-specific selection using estimates of longevity and lifetime reproductive success. Body mass and horn volume showed significant additive genetic variance in both sexes, and intersexual genetic correlations were 0.24+/-0.28 for horn volume and 0.63+/-0.30 for body mass. For horn volume, selection coefficients did not significantly differ from zero in either sex. For body weight, selection coefficients were positive in females but did not differ from zero in males. The absence of detectable sexually antagonistic selection suggests that currently there are no sexual conflicts at loci influencing horn volume and body mass.     

Stability of genetic variance and covariance for reproductive characters in the face of climate change in a wild bird population

Global warming has had numerous effects on populations of animals and plants, with many species in temperate regions experiencing environmental change at unprecedented rates. Populations with low potential for adaptive evolutionary change and plasticity will have little chance of persistence in the face of environmental change. Assessment of the potential for adaptive evolution requires the estimation of quantitative genetic parameters, but it is as yet unclear what impact, if any, global warming will have on the expression of genetic variances and covariances. Here we assess the impact of a changing climate on the genetic architecture underlying three reproductive traits in a wild bird population. We use a large, long-term, data set collected on great tits (Parus major) in Wytham Woods, Oxford, and an 'animal model' approach to quantify the heritability of, and genetic correlations among, laying date, clutch size and egg mass during two periods with contrasting temperature conditions over a 40-year period (1965-1988 [cooler] vs. 1989-2004 [warmer]). We found significant additive genetic variance and heritability for all traits under both temperature regimes. We also found significant negative genetic covariances and correlations between clutch size and egg weight during both periods, and among laying date and clutch size in the colder years only. The overall G matrix comparison among periods, however, showed only a minor difference among periods, thus suggesting that genotype by environment interactions are negligible in this context. Our results therefore suggest that despite substantial changes in temperature and in mean laying date phenotype over the last decades, and despite the large sample sizes available, we are unable to detect any significant change in the genetic architecture of the reproductive traits studied.     

Exploration of cytoplasmic inheritance as a contributor to maternal effects in Welsh Mountain sheep

Cytoplasmic effects were investigated using a dataset comprising three breeding groups of Welsh Mountain sheep. The influences of cytoplasmic effects were investigated by comparing animal models with and without a random term representing cytoplasmic effects. The models were applied to the eight-week weight, scan weight (mean 152 days) and ultrasonically scanned muscle and fat depth. The animal model included the random effects of animals and the maternal additive genetic, maternal permanent environmental and maternal common environmental effects. In total there were 24 569, 10 509, 8389, 8369 records for the eight-week weight, scan weight, muscle depth and fat depth respectively. Four subsets were further analysed containing maternal lines with at least five, ten, fifteen and twenty animals/line. There was no evidence of cytoplasmic effects on eight-week weight and muscle depth. Cytoplasmic effects contributed 1–2% of phenotypic variance for scan-weight and fat depth, but the effect was generally non-significant (P > 0.05). As the number of animals per maternal line increased, the magnitude of cytoplasmic effects also increased for these traits. Direct heritability estimates for the eight-week weight, scan weight, muscle depth and fat depth using the full dataset were 0.18, 0.25, 0.24, and 0.21 respectively.     

Why h2 does not always equal VA/VP?

Over the last decade, there has been a rapid growth in the application of quantitative genetic techniques to evolutionary studies of natural populations. Whereas this work yields enormous insight into evolutionary processes in the wild, the use of modelling techniques and strategies adopted from animal breeders means that estimates of trait heritabilities (h(2)) are highly vulnerable to misinterpretation. Specifically, when estimated using animal models, h(2) will not generally be comparable across studies and must be interpreted as being conditioned on any fixed effects included in the model. Failure to realize the model dependency of published h(2) estimates will give a very misleading, and in most cases upwardly biased, impression of the potential for trait evolution.     

籼稻稻米外观品质的细胞质,母体和胚乳遗传效应分析

利用浙协2号A等9个籼型不育系和T49等5个籼型恢复系进行不完全双列杂交,研究了籼稻稻米外观品质的遗传效应．结果表明,稻米外观品质性状的表现受制于胚乳、母体和细胞质三套遗传体系．糙米长、长宽比和长厚比等性状以母体遗传率为主,而糙米宽和糙米厚则以胚乳直接遗传率为主,糙米长和长宽比等性状的细胞质遗传率亦很重要．结果还发现外观品质性状间存在着较强的遗传相关,其中糙米长与糙米宽、糙米长与糙米厚、糙米宽与糙米厚、糙米宽与长宽比、糙米厚与长厚比以及糙米长宽比与长厚比性状间以胚乳直接加性和母体加性相关为主．而糙米长与长宽比、糙米长与长厚比、糙米宽与长厚比以及糙米厚与长宽比性状间则以胚乳直接显性和母体显性相关为主．就外观品质的总体情况而言,遗传效应预测值表明参试亲本以V20A、作5A和测早2-2较好,其各种遗传效应能够显著改善稻米品质性状。V20A／102和作5A／测早2-2等组合具有较好的稻米外观品质．